3t(t+2)=1

Solution for 3t(t+2)=1 equation:

Simplifying
3t(t + 2) = 1

Reorder the terms:
3t(2 + t) = 1
(2 * 3t + t * 3t) = 1
(6t + 3t2) = 1

Solving
6t + 3t2 = 1

Solving for variable 't'.

Reorder the terms:
-1 + 6t + 3t2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 6t + 3t2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-0.3333333333 + 2t + t2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 2t + 0.3333333333 + t2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 2t + t2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 2t + t2 = 0 + 0.3333333333
2t + t2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
2t + t2 = 0.3333333333

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 0.3333333333 + 1

Reorder the terms:
1 + 2t + t2 = 0.3333333333 + 1

Combine like terms: 0.3333333333 + 1 = 1.3333333333
1 + 2t + t2 = 1.3333333333

Factor a perfect square on the left side:
(t + 1)(t + 1) = 1.3333333333

Calculate the square root of the right side: 1.154700538

Break this problem into two subproblems by setting 
(t + 1) equal to 1.154700538 and -1.154700538.

Subproblem 1
t + 1 = 1.154700538

Simplifying
t + 1 = 1.154700538

Reorder the terms:
1 + t = 1.154700538

Solving
1 + t = 1.154700538

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + t = 1.154700538 + -1

Combine like terms: 1 + -1 = 0
0 + t = 1.154700538 + -1
t = 1.154700538 + -1

Combine like terms: 1.154700538 + -1 = 0.154700538
t = 0.154700538

Simplifying
t = 0.154700538

Subproblem 2
t + 1 = -1.154700538

Simplifying
t + 1 = -1.154700538

Reorder the terms:
1 + t = -1.154700538

Solving
1 + t = -1.154700538

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + t = -1.154700538 + -1

Combine like terms: 1 + -1 = 0
0 + t = -1.154700538 + -1
t = -1.154700538 + -1

Combine like terms: -1.154700538 + -1 = -2.154700538
t = -2.154700538

Simplifying
t = -2.154700538

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.154700538, -2.154700538}